Concept:Ripple factor is the ratio of the effective (RMS) value of the AC ripple components to the pure DC output voltage.
Formula:$$\gamma = \frac{V_{\text{ac, rms}}}{V_{\text{dc}}} = \frac{\sqrt{V_{\text{rms}}^2 - V_{\text{dc}}^2}}{V_{\text{dc}}} = \sqrt{\left(\frac{V_{\text{rms}}}{V_{\text{dc}}}\right)^2 - 1}$$
Solution:- Because total RMS voltage consists of orthogonal AC and DC parts (\( V_{\text{rms}}^2 = V_{\text{dc}}^2 + V_{\text{ac, rms}}^2 \)):
- $$V_{\text{ac, rms}} = \sqrt{V_{\text{rms}}^2 - V_{\text{dc}}^2}$$
- Dividing by \( V_{\text{dc}} \) gives \( \gamma = \sqrt{(V_{\text{rms}}/V_{\text{dc}})^2 - 1} \).
Why other options are incorrect:- Option A: This is the DC form factor ratio.
- Option B: \( V_{\text{rms}}/V_{\text{dc}} \) is the total form factor \( F \), not the ripple factor.
- Option D: Inverts the terms inside the square root.
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